In recent years, the development of a light-emitting device is remarkable which adopts a III-V compound (hereinafter, referred to as “nitride”) or II-VI compound formed with a quantum well therein and generates light by binding electrons with holes respectively in the quantum well with electric current applied from outside.
A material which is used mostly as the III-V compound is a GaN of the nitride. Commencing with the GaN, the refractive index of the nitride is larger than 1. Accordingly, there is a problem in extracting light from a light-emitting device to the atmosphere. For example, in the case of the GaN as an example, the refractive index is about 2.5. Accordingly, light incident to a normal line on a boundary between the GaN and the atmosphere at an angle which is larger than a predetermined angle (for example, 23.6 degrees) is not emitted to the atmosphere but totally reflected on the boundary surface and trapped in a GaN layer in the light-emitting device. Hereinafter, a conical area formed in an area having an angle smaller than a predetermined angle with respect to the normal line is referred to as an “escape cone.”
Most part of light trapped in the GaN layer is reabsorbed in a crystal and an electrode material and changed to a heat, and is not extracted to outside. Therefore, there is a problem that the light-extraction efficiency is not improved when a flat GaN layer is used.
Therefore, with respect to such problem, the Patent Document 1 discloses, as shown in FIG. 34, a technology of forming rectangular recesses and projections having a pitch of 2 to 4 μm and a depth of λ*(2n+1)/4(n=1, 2, . . . ) on a light-extraction surface through which the light from the light-emitting device is emitted. According to this technology, light rays reflected respectively on the recesses and projections eliminate each other by having a difference of λ/2 in a phase. Accordingly, the light reflected on the light-extraction surface is reduced. Consequently, the light-extraction efficiency can be improved.
Further, the Patent Document 2 discloses, as shown in FIG. 35, a technology of forming a periodically ordered boundary face structure on a predetermined boundary face of an LED to improve the light-extraction efficiency. According to this technology, the light-extraction efficiency of light incident at an angle equal to or larger than the total reflection angle is improved. In accordance with a shape, doubled light-extraction efficiency can be obtained as compared to the case where there is no such structure.
Here, it is known that the light-extraction efficiency of light extracted from one boundary face or surface in the case where there is no normal surface shape can be given by n22/4*n12 when it is taking in consideration a solid angle of the escape cone and given that n1 being a refractive index of a portion including a light-emitting layer and n2 being a refractive index of an outer portion. Thus, in the case where a semiconductor layer is the GaN and its exterior is air, the light-extraction efficiency is calculated to be 4% since it is given that n1=2.5, n2=1. Further, if the light is extracted from all of the surfaces other than the bottom surface, and the structure is formed only on the upper surface so that the doubled light-extraction efficiency is obtained, a light-extraction efficiency of 24%=4*4 (side surfaces)+4*2 (doubled as the upper surface having recesses and projections) can be obtained.
Further, the Non-Patent Document 1 discloses, as shown in FIG. 36, a technology of forming a random texture or applying a rough finishing onto a surface of a semiconductor LED. According to this technology, an angular distribution of a light ray in the device is made random by the random texture formed on the surface. After taking multiple paths in accordance with the device structure, a possibility that the light escapes becomes high. Consequently, the light-extraction efficiency can be improved. It should be noted that a hatched layer in FIG. 36 is an active layer.
However, according to the respective methods shown in the Patent Documents 1, 2, light incident at an angle equal to or larger than the total reflection angle is not extracted from the GaN. Accordingly, there is a predetermined limit in improvement of the light-extraction efficiency. Further, since the recesses and projections are formed on the surface, the incident angle of light extracted from one point light source becomes wider as compared to the flat surface. However, the light-extraction efficiency at an angle where the light is essentially emitted is reduced. Accordingly, merely double at most in improvement in the light-extraction efficiency can be obtained.
Further, the Patent Document 2 also discloses a method for improving the light-extraction efficiency by adopting a resonator structure to limit distribution of emitted light to be within the escape cone. However, since the resonator structure is adopted in this method, accuracy in a resonator length (thickness of a semiconductor layer) is required. Accordingly, it becomes difficult to improve an extraction rate. Further, in the resonator structure, controlling all of the emitted light to be within the escape cone is fundamentally impossible, and improvement in the light-extraction efficiency is limited to about 50%.
Further, in the technology of the Non-Patent Document 1, a light ray taking multiple paths is absorbed by a reflective layer such as an electrode and reduces its strength drastically before it escapes. Further, even if a reflectance of the reflective layer is improved, the light-extraction efficiency may be rather reduced in the case where not only a pitch but also a shape is random, as can be seen in FIG. 36. Accordingly, the light-extraction efficiency is not improved. This fact is confirmed by experiments performed by the inventors of the present invention. In the experiment, a random and rough shape of surface obtained by applying a wet etching to polycrystal silicon is transferred onto and duplicated on the light-extraction surface.    Patent Document 1: Japanese Unexamined Patent Publication No. HEI07-202257    Patent Document 2: Japanese Unexamined Patent Publication No. HEI10-4209    Non-Patent Document 1: Schnitzer, et al. In Applied Physics Letters 63, 2174 (1993)